This Voronoi hierarchy image of the Cat's Eye Nebula contains 737 cells. The second elliptical path in the center is now evident. This is the second image in a series of three Voronoi hierarchy images. [Second in a series of 3 related images. See Image 3.]

More about this Image
A Voronoi hierarchy is a new, general form of multi-resolution hierarchies. The method can be applied to a variety of data, including scattered data, arbitrarily gridded data and data on multi-dimensional domains. To create a Voronoi hierarchy, an initial Voronoi diagram must first be created to represent the coarsest level of detail. Second, points are inserted into the existing diagram to create higher levels of resolution. At each iteration of the algorithm, we identify a set of cells with high errors. Inserting points where the maximal errors occur leads to excellent results. The series show three resolutions of a Voronoi hierarchy. The first level contains 208 cells; the second contains 737 cells; and the final, 8284 cells. Using this algorithm, we can generate an excellent representation of the original image at a fraction of the original data size.

This work was supported in part by the National Science Foundation Large Scientific and Software Data Set Visualization program under grant ACI 99-82251. (Year of image: 1999)